1. To have incriminating or unfavorable proof against one, as for some crime, wrongdoing, or misbehavior. Go to the police, for all I care! You don't have anything on me! If we want to nail him for fraud, we'll need to have more on him than a few questionable phone calls.

2. To have a particular advantage over one. You may think you can beat me, but I've got 10 years' experience on you.

3. To currently be in possession of something. Hey, do you have a pen on you? I need to write this down. Yeah, I have a tissue on me.